A Methodology for Simulations of Complex Turbulent Flows

Abstract

A new flow simulation methodology (FSM) for computing turbulent shear flows is presented. The development of FSM was initiated in close collaboration with C. Speziale (then at Boston University). The centerpiece of FSM is a strategy to provide the proper amount of modeling of the subgrid scales. The strategy is implemented by use of a “contribution function” which is dependent on the local and instantaneous “physical” resolution in the computation. This physical resolution is obtained during the actual simulation by comparing the size of the smallest relevant scales to the local grid size used in the computation. The contribution function is designed such that it provides no modeling if the computation is locally well resolved so that the computation approaches a direct numerical simulation in the fine grid limit, or provides modeling of all scales in the coarse grid limit and thus approaches an unsteady RANS calculation. In between these resolution limits, the contribution function adjusts the necessary modeling for the unresolved scales while the larger (resolved) scales are computed as in traditional large-eddy simulations (LES). However, a LES that is based on the present strategy is distinctly different from traditional LES in that the required amount of modeling is determined by physical considerations, and that state-of-the-art turbulence models (as developed for Reynolds-averaged Navier-Stokes) can be employed for modeling of the unresolved scales. Thus, in contrast to traditional LES based on the Smagorinsky model, with FSM a consistent approach (in the local sense) to the coarse grid and fine grid limits is possible. As a consequence of this, FSM should require much fewer grid points for a given calculation than traditional LES or, for a given grid size, should allow computations for larger Reynolds numbers. In the present paper, the fundamental aspects of FSM are presented and discussed. Several examples are provided. The examples were chosen such that they expose, on the one hand, the inherent difficulties of simulating complex wall bounded flows, and on the other hand demonstrate the potential of the FSM approach.

Modeling of turbulent, isothermal and cryogenic cavitation under attached conditions

“…Essentially, based on the numerical resolutions available in a given computational set-up, it adaptively adjusts the use of the eddy viscosity. Following Ruprecht et al [57], Fasel et al [60], and Johansen et al [61], the general idea is to limit the influence of the eddy viscosity based on the local numerical resolution, essentially forming a combined direct numerical simulation and RANS model. Specifically, the level of the turbulent viscosity is corrected by comparing the turbulence length scale (k 3/2 /ε) and the filter size , which is based on the local meshing spacing.…”

Tandem cylinder flow and noise predictions using a hybrid RANS/LES approach

“…Since this hybrid approach is distinctly different from other RANS/LES methods, it was referred to as Flow Simulation Methodology (FSM) by subsequent authors [6,7]. One of the issues with the FSM approach is that of consistency, which was not addressed by Speziale [4] or subsequent FSM-based publications and deals with how the Reynolds-stress tensor τ…”

Simulation of Supersonic Base Flows: Numerical Investigations Using DNS, LES, and URANS

“…Other forms of the contribution function and different choices of the length-scale are possible (see, e.g. Fasel et al, 2002).…”

“…Another approach, that smoothly blends DNS, LES and RANS has been suggested by Speziale (1998a,b) and was named the Flow Simulation Methodology (FSM) (for details, see review papers by Fasel et al, 2002Fasel et al, , 2006. The centerpiece of FSM is a strategy to provide a proper amount of modelling of the subgrid scales based on the "local and time-instantaneous physical resolution" of the calculation.…”